Chapter 4 4.2. Description of the case study
Actuator force measurement
As well as applying a certain force, the servo-hydraulic actuators are also able to send a force feedback to the controller through the load cells included.
Actuator displacement measurement
Two devices are used to measure the displacement of the actuator: the actuator internal sensor and an external laser. For vertical actuators, the displacements are measured via the internal sensor while the laser devices are just used to check the measurements.
Digital image correlation
Digital image correlation (DIC) is an optical measurement technique for capturing, tracking and measuring deformations and strains on the specimen surface compar-ing processed images of the specimen surface at different instants of time.
Linear variable displacement transducers
Linear variable displacements transducers (LVDTs) are mounted to the specimen surface in order to punctual monitor its deformations.
4.2. Description of the case study Chapter 4
Figure 4.3: Masonry wall
Table 4.1: Material specifications of clay brick Swiss K-Modul 15/19 [28]
Clay brick Swiss K-Modul 15/19
Length 290 mm
Width 150 mm
Height 290 mm
Void ratio 25− 55 %
Rate of water absorption < 3.5 m2kgmin
Gross bulk density N P D
Compressive strength fb 28 MPa
Bond strength 0.16 MPa
Water vapor permeability µ 4
The cement mortar characteristic bending and compressive strengths are deter-mined according to SN EN 196-1:2016 through bending and compressive testing performed on six cuboid mortar specimens of 40 ⇥ 40 ⇥ 160 mm size and a storage time age of 62 days. Specifically, three samples (K1, K2 & K3) were stored in a climate room (constant air humidity at 95%), the others (S1, S2 & S3) were kept at the making site (laboratory) where the masonry walls for the Hybrid Simulation were built and stored. The setups used for the tests are shown in Figure 4.4 [28], while the test results of the samples stored in the climate room (K) and at the making site (S) are shown in Table 4.3 [28].
According to SN EN 1052-1:1998, compression test on three masonry specimens built and stored at the making site of 0.59 ⇥ 0.15 m2 nominal cross-section and 1 m height and with a bed joint thickness of approximately 10 mm, were performed in order to determine the compressive strength and the modulus of elasticity of the
Chapter 4 4.2. Description of the case study Table 4.2: Compression test results of clay bricks [28]
Sample Fmax [kN] fbk [MPa]
1 985.0 22.7
2 1195.9 27.1
3 1194.0 27.1
4 760.9 17.4
5 871.1 19.9
6 1099.9 25.1
7 1123.9 25.7
8 1001.7 23.2
9 1185.8 27.1
10 1108.4 25.5
Average 1052.7 24.1
Std. deviation 3.3
Table 4.3: Test results of mortar samples [28]
Sample fmq [MPa] fm [MPa]
K1 4.71 15.36
14.17
K2 4.77 15.48
17.12
K3 4.42 15.25
14.27
Average 4.63 14.90
Std. dev. 0.19 0.63
Sample fmq [MPa] fm [MPa]
S1 1.09 2.73
S2 0.96 2.652.86
2.95
S3 1.12 2.65
2.43
Average 1.06 2.77
Std. dev. 0.09 0.13
masonry used for the Hybrid Simulation tests. The test was conducted in force control mode until failure, with a ramp rate of 27 kN/min [28]. The displacements on the specimen surface were measured to determine the strains arising during the compression test by one horizontal and two vertical linear variable displacement transducers (LVDTs) mounted on each side of the specimen. The test setup is rep-resented in Figure 4.5, whereas the results of the compression test are summarized in Table 4.4. Finally, Table 4.5 presents a summary of all material properties.
4.2.2 Hybrid simulations
The PSD-HS architecture setup used in the case study is shown in Figure 4.6.
In detail, a steel beam interfaces three servo-hydraulic actuators of 1 MN capacity each to the wall specimen, while 11 LVDTs are used to measure three types of displacements: sliding, uplift and vertical deformations. Furthermore, during the tests, a DIC system (NIKON D810 digital camera - 50 mm lens) acquires the in-plane displacements of the wall surface prior painted with a random speckle
4.2. Description of the case study Chapter 4
Figure 4.4: Bending and compressive strength testing [28]
Test setup:
1) steel beam 2) masonry specimen 3) wood fibre layer LVDT positions:
a) SL or NL b) SM or NM c) SR or NR 1)
2)
3) 1)
3)
a) c)
b)
x
y
Fmax fxk Ex
kN MPa GPa
460.47 5.20 4.51 421.89 4.77 4.01
Figure 4.5: Test setup for compression test of masonry specimens [28]
61
Chapter 4 4.2. Description of the case study Table 4.4: Compression test results of masonry specimens [28]
Specimens Fmax [kN] fxk [MPa] Exk [GPa]
R1 460.47 5.20 4.51
R2 421.89 4.77 4.01
R3 482.69 5.45 4.10
Average 455.02 5.14 4.21
Table 4.5: Material properties [28]
Material fmq [MPa] fbk [MPa] Exk [MPa]
Brick − 24.1 −
Mortar (K) 4.63 14.9 −
Mortar (S) 1.06 2.77 −
Masonry − 5.14 4.21
pattern, shooting planar black & white pictures every 2 sec (Figure 4.7).
In order to perform PSD-HS of the system, the actuator setup was interfaced to an INDEL GIN-SAM4 real-time computer via Ether CAT. Before starting the PSD-HS experiment, a vertical load ramp was imposed to the specimen up to 208 kN corresponding to the nominal vertical load. Then, the INDEL GIN-SAM4 real-time computer executes the time integration algorithm, sends actuator dis-placement commands to the INOVA controller and reads corresponding feedback forces measured with loads cells at each time step of the simulation [53]. Detailed description of the time integration algorithm used in this testing campaign can be found in [13] and [57].
In Table 4.6 the experimental test campaign of the six Hybrid Simulations is summarized. A record of the Montenegro earthquake (1979) was selected from the PEER Ground Motion Database (PEER, 2018), as seismic excitation and scaled to different values of PGA (Figure 4.8). The so determined accelerograms were fed into the equations of motion as seismic excitation, thus defining the displacement path of the horizontal actuator (horizontal loading under displacement control conditions).
The first two experiments, Test #1a and #1b, were conducted considering a small value of PGA to guarantee a linear response of the PS. The difference between these two tests was in the testing time scale. They were carried out in order to chose which was the best suited prototype structure to prevent dynamic instability due to experimental errors. So that, all following experiments were conducted on SM1 structures (4-DoFs NS and a λ = 200) [53]. During Test #2 a linear response was observed, while slightly nonlinear responses characterized Tests #3 and #4 although damage accumulation was very small. Detailed description of the tests can be found in [53]. The focus of this thesis work relies on Test #5 specifically, which was stopped earlier (after approximately 2.5 s of simulation time, i.e. 500 s
4.2. Description of the case study Chapter 4
Figure 4.6: Architecture of the PSD-HS setup [28]
mm
Figure 4.7: Test setup for DIC analysis [28]
Chapter 4 4.2. Description of the case study Hybrid simulation techniques in the structural analysis and testing of architectural heritage
134
masonry facade was subjected to a nominal vertical load of 208 kN, that corresponds to 10% of the compressive strength of masonry uniformly distributed over a cross section of 2.7x0.15 m. A record of the Montenegro earthquake (1979) was selected from the PEER Ground Motion Database (PEER), (P.PEERC, 2013), as seismic excitation and scaled to different values of Peak Ground Acceleration (PGA).
Figure 74 depicts both the selected seismic record and related acceleration response spectrum. In order to support the design of the experimental campaign and the derivation of both substructure matrices, two FE models of the masonry facade, namely Reference Model (RM) -1 and -2, were implemented in Matlab based on 4-node plate elements, (Matlab, 2010).
(a) (b)
Figure 74: The 1979 Montenegro earthquake: (a) ground motion record scaled to 6.36 m/s2 PGA; and (b) corresponding acceleration response spectrum for 3.00 % viscous damping.
In detail, RM1 represents the idealized masonry facade while RM2 describes its hybrid model, which is characterized by a rigid interface between NS and PS.
Both FE models are characterized by 468 DoFs but additional 2-nodes rigid beam elements enforce rigid behaviour at both substructure interfaces in RM2, as depicted in Figure 75.
Table 19 compares modal frequencies of RM1 and RM2 while Table 20 reports MAC values calculated for each pairs of corresponding deformational shapes, (Allemang & Brown, 1982). As can be appreciated, modal characteristics are almost unaltered up to mode 4. In order to testify that this was sufficient for preserving the seismic response of RM1, Figure 76 compares displacement response histories of RM1 and RM2 measured at Node 111 along X and Y directions. Time history analyses were performed with the Newmark algorithm, (Newmark, 1959), considering 3.00 % equivalent viscous damping and 1 msec time step. Accordingly, mass and stiffness matrices of both PS and NS were derived from RM2 as explained in the following section.
Table 19:Comparison of modal frequencies.
Mode fRM1 [Hz] fRM2 [Hz]
Figure 4.8: 1979 Montenegro earthquake Table 4.6: Test program [53]
ID PGA [m/s2] λ Prototype structure freq. b.w. [Hz]
#1a 0.45 500 SM2 (7-DoFs NS) 0÷ 0.55
#1b 0.45 200 SM2 (7-DoFs NS) 0÷ 1.38
#2 1.82 200 SM1 (4-DoFs NS) 0÷ 0.56
#3 3.18 200 SM1 (4-DoFs NS) 0÷ 0.56
#4 3.18 200 SM1 (4-DoFs NS) 0÷ 0.56
#5 6.36 200 SM1 (4-DoFs NS) 0÷ 0.56
of wall-clock time) than the duration of the ground motion owing to the collapse of the wall specimen.
Figure 4.9 depicts the hysteresis loops of the horizontal and vertical restoring forces measured by the actuators. Five milestones (T1, T2, T3, T4, T5) are pointed out on the figure referring to specific evolution of the specimen collapse. While in Figure 4.10 are shown the displacements recorded during the collapse test.
It is worth to underlying as well that all plots refer to simulation time, which corresponds to wall-clock time divided by testing time scale.
For each milestone, Figure 4.11 depicts the Von Mises strain field measured via DIC. At T1 (about 1.2 s), von Mises strain concentrates at the lower mortar joint of the left wall bay and along a diagonal path following the mortar joints of the upper left part of the wall starting from the upper left corner of the opening.
Such von Mises strain concentrations indicate joint opening, which allows relative rocking between wall subparts. Between T1 and T2 (about 1.45 s), the wall expe-rience horizontal loading reversal, the lower left mortar joint closes and von Mises strain concentrations arise at both the lower and the upper levels of the thinner right wall bay. At T3 (about 1.75 s), remarkable von Mises strain concentrations are visible on both left and right lower mortar joints as well as along a diagonal path that connects the upper left corner of the opening to the upper mortar joint.
At this point, joint opening allows relative rocking of three facade blocks namely, left and right bays and the spandrel. Suddenly, at T4 (about 2.2 s), the thinner wall bay spits at the level of the upper mortar joint and detaches from the spandrel,
4.2. Description of the case study Chapter 4
(a) Vertical south actuators (b) Vertical north actuators
(c) Horizontal south actuators
Figure 4.9: Restoring forces hysteresis loops measured during Test #5
which starts uplifting. The right edge of the spandrel rotates in clock-wise between T4 and T5 (about 2.4s) and impacts the thinner wall bay, which crashes under compressive load as testified by the large diagonal crack visible at the end of the experiment. The test stops immediately afterwards [53].
Finally, Figure 4.12 shows the specimen after Test #5 and a close-up view on critical regions where damage concentrated.
Chapter 4 4.2. Description of the case study
(a) Horizontal displacement (b) Vertical displacement
(c) LVDT displacements (SS-SN) (d) LVDT displacements (UN1-UN2)
(e) LVDT displacements (US1-US2) (f) LVDT displacements (VN-VS-VM) Figure 4.10: Displacement responses during Test #5
4.2. Description of the case study Chapter 4
(a) Milestone T1 (b) Milestone T2
(c) Milestone T3 (d) Milestone T4
(e) Milestone T5
Figure 4.11: Von Mises strain field measured via DIC during Test #5
Chapter 4 4.2. Description of the case study
Gaetano Miraglia
149
(b) (c)
(d) (e)
Figure 87: Von Mises strain field in [mm/mm] measured via DIC during Test #5 at milestones: (a) T1; (b) T2; (c) T3; (d) T4; and (e) T5.
Figure 88: Overview of the wall specimen after Test #5: front view (upper left), right wall bay (upper right), left wall bay (bottom left) and bottom left corner (bottom right).Figure 4.12: Overview of the wall specimen after Test #5
Chapter 5
NARX model for the masonry facade case study
Despite the high generality of surrogate modelling and Bayesian inversion, when such techniques are applied to data coming from experimental tests, additional effort in the posedness of the problem is needed. For this reason this chapter fo-cuses on the definition of best regressors suitable for the case study introduced in Chapter 4. In Section 5.1 an holonomic model for mortar joints is briefly introduced theoretically. Then the FE model of the masonry structure and its parameterization is presented pointing out how model parameters variability influ-ence the model response (Section 5.2). Finally, in Section 5.3 a set of NARX basis terms are proposed as best regressor suitable for the underlying problem.